#include <TColStd_Array1OfReal.hxx>
#include <ExprIntrp_GenExp.hxx>
+#include <CASCatch_CatchSignals.hxx>
+#include <CASCatch_Failure.hxx>
+#include <CASCatch_ErrorHandler.hxx>
+#include <OSD.hxx>
+#include <math_GaussSingleIntegration.hxx>
+
#include <string>
#include <math.h>
}
}
-/*!
- * \brief This class provides interface for a density function
- */
-class Function
+class Function
{
public:
- Function(bool expMode) : _expMode(expMode) {}
- double operator() (double t) const;
- virtual bool IsReady() const = 0;
-protected:
- virtual double compute(double t) const = 0;
+ Function( const bool exp )
+ : myExp( exp )
+ {
+ }
+
+ virtual ~Function()
+ {
+ }
+
+ virtual bool value( const double, double& f )
+ {
+ if( myExp )
+ f = pow( 10, f );
+ return true;
+ }
+ virtual double integral( const double, const double ) = 0;
+
private:
- bool _expMode;
+ bool myExp;
};
-/*!
- * \brief This class provides computation of density function given by a table
- */
-class TabFunction: public Function
+class FunctionIntegral : public Function
{
public:
- TabFunction(const vector<double>& table, bool expMode);
- virtual bool IsReady() const;
-protected:
- virtual double compute(double t) const;
+ FunctionIntegral( Function*, const double );
+ virtual ~FunctionIntegral();
+ virtual bool value( const double, double& );
+ virtual double integral( const double, const double );
+
private:
- const vector<double>& _table;
+ Function* myFunc;
+ double myStart;
};
-/*!
- * \brief This class provides computation of density function given by an expression
- */
-class ExprFunction: public Function
+FunctionIntegral::FunctionIntegral( Function* f, const double st )
+: Function( false )
+{
+ myFunc = f;
+ myStart = st;
+}
+
+FunctionIntegral::~FunctionIntegral()
+{
+}
+
+bool FunctionIntegral::value( const double t, double& f )
+{
+ f = myFunc ? myFunc->integral( myStart, t ) : 0;
+ return myFunc!=0 && Function::value( t, f );
+}
+
+double FunctionIntegral::integral( const double, const double )
+{
+ return 0;
+}
+
+class FunctionTable : public Function
{
public:
- ExprFunction(const char* expr, bool expMode);
- virtual bool IsReady() const;
-protected:
- virtual double compute(double t) const;
+ FunctionTable( const std::vector<double>&, const bool );
+ virtual ~FunctionTable();
+ virtual bool value( const double, double& );
+ virtual double integral( const double, const double );
+
private:
- Handle(Expr_GeneralExpression) _expression;
- Expr_Array1OfNamedUnknown _var;
- mutable TColStd_Array1OfReal _val;
+ bool findBounds( const double, int&, int& ) const;
+
+ //integral from x[i] to x[i+1]
+ double integral( const int i );
+
+ //integral from x[i] to x[i]+d
+ //warning: function is presented as linear on interaval from x[i] to x[i]+d,
+ // for correct result d must be >=0 and <=x[i+1]-x[i]
+ double integral( const int i, const double d );
+
+private:
+ std::vector<double> myData;
};
-double Function::operator() (double t) const
+FunctionTable::FunctionTable( const std::vector<double>& data, const bool exp )
+: Function( exp )
{
- double res = compute(t);
- if (_expMode)
- res = pow(10, res);
- return res;
+ myData = data;
}
-TabFunction::TabFunction(const vector<double>& table, bool expMode)
- : Function(expMode),
- _table(table)
+FunctionTable::~FunctionTable()
{
}
-bool TabFunction::IsReady() const
+bool FunctionTable::value( const double t, double& f )
{
+ int i1, i2;
+ if( !findBounds( t, i1, i2 ) )
+ return false;
+
+ double
+ x1 = myData[2*i1], y1 = myData[2*i1+1],
+ x2 = myData[2*i2], y2 = myData[2*i2+1];
+
+ Function::value( x1, y1 );
+ Function::value( x2, y2 );
+
+ f = y1 + ( y2-y1 ) * ( t-x1 ) / ( x2-x1 );
return true;
}
-double TabFunction::compute (double t) const
+double FunctionTable::integral( const int i )
{
- //find place of <t> in table
- int i;
- for (i=0; i < _table.size()/2; i++)
- if (_table[i*2] > t)
- break;
- if (i >= _table.size()/2)
- i = _table.size()/2 - 1;
-
- if (i == 0)
- return _table[1];
-
- // interpolate function value on found interval
- // (t - x[i-1]) / (x[i] - x[i-1]) = (y - f[i-1]) / (f[i] - f[i-1])
- // => y = f[i-1] + (f[i] - f[i-1]) * (t - x[i-1]) / (x[i] - x[i-1])
- double x1 = _table[(i-1)*2];
- double x2 = _table[i*2];
- double y1 = _table[(i-1)*2+1];
- double y2 = _table[i*2+1];
- if (x2 - x1 < Precision::Confusion())
- throw SALOME_Exception("TabFunction::compute : confused points");
- return y1 + (y2 - y1) * ((t - x1) / (x2 - x1));
+ if( i>=0 && i<myData.size()-1 )
+ return integral( i, myData[2*(i+1)]-myData[2*i] );
+ else
+ return 0;
}
-ExprFunction::ExprFunction(const char* expr, bool expMode)
- : Function(expMode),
- _var(1,1),
- _val(1,1)
+double FunctionTable::integral( const int i, const double d )
{
- Handle( ExprIntrp_GenExp ) gen = ExprIntrp_GenExp::Create();
- gen->Process(TCollection_AsciiString((char*)expr));
- if (gen->IsDone())
- {
- _expression = gen->Expression();
- _var(1) = new Expr_NamedUnknown("t");
- }
+ double f, res = 0.0;
+ if( value( myData[2*i]+d, f ) )
+ res = ( myData[2*i] + f ) / 2.0 * d;
+
+ return res;
}
-bool ExprFunction::IsReady() const
+double FunctionTable::integral( const double a, const double b )
{
- return !_expression.IsNull();
+ int x1s, x1f, x2s, x2f;
+ findBounds( a, x1s, x1f );
+ findBounds( b, x2s, x2f );
+ double J = 0;
+ for( int i=x1s; i<x2s; i++ )
+ J+=integral( i );
+ J-=integral( x1s, a-myData[2*x1s] );
+ J+=integral( x2s, b-myData[2*x2s] );
+ return J;
}
-double ExprFunction::compute (double t) const
+bool FunctionTable::findBounds( const double x, int& x_ind_1, int& x_ind_2 ) const
{
- ASSERT(!_expression.IsNull());
- _val(1) = t;
- return _expression->Evaluate(_var, _val);
+ int n = myData.size();
+ if( n==0 || x<myData[0] )
+ {
+ x_ind_1 = x_ind_2 = 0;
+ return false;
+ }
+
+ for( int i=0; i<n-1; i++ )
+ if( myData[2*i]<=x && x<=myData[2*(i+1)] )
+ {
+ x_ind_1 = i;
+ x_ind_2 = i+1;
+ return true;
+ }
+ x_ind_1 = n-1;
+ x_ind_2 = n-1;
+ return false;
}
-//================================================================================
-/*!
- * \brief Compute next abscissa when two previous ones are given
- * \param sm2 - before previous abscissa
- * \param sm1 - previous abscissa
- * \param func - function of density
- * \param reverse - the direction of next abscissa, increase (0) or decrease (1)
- * \retval double - the new abscissa
- *
- * The abscissa s is given by the formulae
- *
- * ....|--------|----------------|.....
- * sm2 sm1 s
- *
- * func(sm2) / func(sm1) = (sm1-sm2) / (s-sm1)
- * => (s-sm1) * func(sm2) = (sm1-sm2) * func(sm1)
- * => s = sm1 + (sm1-sm2) * func(sm1) / func(sm2)
- */
-//================================================================================
-static double nextAbscissa(double sm2, double sm1, const Function& func, int reverse)
+
+class FunctionExpr : public Function, public math_Function
{
- if (reverse)
- {
- sm1 = 1.0 - sm1;
- sm2 = 1.0 - sm2;
- }
- return sm1 + (sm1-sm2) * func(sm1) / func(sm2);
+public:
+ FunctionExpr( const char*, const bool );
+ virtual ~FunctionExpr();
+ virtual Standard_Boolean Value( Standard_Real, Standard_Real& );
+ virtual bool value( const double, double& ); //inherited from Function
+ virtual double integral( const double, const double );
+
+private:
+ Handle(ExprIntrp_GenExp) myExpr;
+ Expr_Array1OfNamedUnknown myVars;
+ TColStd_Array1OfReal myValues;
+};
+
+FunctionExpr::FunctionExpr( const char* str, const bool exp )
+: Function( exp ),
+ myVars( 1, 1 ),
+ myValues( 1, 1 )
+{
+ myExpr = ExprIntrp_GenExp::Create();
+ myExpr->Process( ( Standard_CString )str );
+ if( !myExpr->IsDone() )
+ myExpr.Nullify();
+
+ myVars.ChangeValue( 1 ) = new Expr_NamedUnknown( "t" );
}
-//================================================================================
-/*!
- * \brief Compute distribution of points on a curve following the law of a function
- * \param C3d - the curve to discretize
- * \param first - the first parameter on the curve
- * \param last - the last parameter on the curve
- * \param theReverse - flag indicating that the curve must be reversed
- * \param nbSeg - number of output segments
- * \param func - the function f(t)
- * \param theParams - output points
- * \retval bool - true if success
- */
-//================================================================================
+FunctionExpr::~FunctionExpr()
+{
+}
-static bool computeParamByFunc(Adaptor3d_Curve& C3d, double first, double last,
- double length, bool theReverse,
- int nbSeg, const Function& func,
- list<double>& theParams)
+Standard_Boolean FunctionExpr::Value( Standard_Real T, Standard_Real& F )
+{
+ double f;
+ Standard_Boolean res = value( T, f );
+ F = f;
+ return res;
+}
+
+bool FunctionExpr::value( const double t, double& f )
{
- if (!func.IsReady())
+ if( myExpr.IsNull() )
return false;
- // ########## TMP until pb division by zero when func(0.0)==0 is fixed #########
- if (::Abs(func(0.0)) <= ::RealSmall() ) return false;
- // ########## TMP until pb division by zero when func(0.0)==0 is fixed #########
+ CASCatch_CatchSignals aCatchSignals;
+ aCatchSignals.Activate();
- vector<double> xxx[2];
- int nbPnt = 1 + nbSeg;
- int rev, i;
- for (rev=0; rev < 2; rev++)
+ myValues.ChangeValue( 1 ) = t;
+ bool ok = true;
+ CASCatch_TRY {
+ f = myExpr->Expression()->Evaluate( myVars, myValues );
+ }
+ CASCatch_CATCH(CASCatch_Failure) {
+ aCatchSignals.Deactivate();
+ Handle(CASCatch_Failure) aFail = CASCatch_Failure::Caught();
+ f = 0.0;
+ }
+
+ aCatchSignals.Deactivate();
+ ok = Function::value( t, f ) && ok;
+ return ok;
+}
+
+double FunctionExpr::integral( const double a, const double b )
+{
+ double res = 0.0;
+ CASCatch_TRY
{
- // curv abscisses initialisation
- vector<double> x(nbPnt, 0.);
- // the first abscissa is 0.0
+ math_GaussSingleIntegration _int( *this, a, b, 20 );
+ if( _int.IsDone() )
+ res = _int.Value();
+ }
+ CASCatch_CATCH(CASCatch_Failure)
+ {
+ res = 0.0;
+ MESSAGE( "Exception in integral calculating" );
+ }
+ return res;
+}
- // The aim of the algorithm is to find a second abscisse x[1] such as the last
- // one x[nbSeg] is very close to 1.0 with the epsilon precision
- double x1_too_small = 0.0;
- double x1_too_large = RealLast();
- double x1 = 1.0/nbSeg;
- while (1)
- {
- x[1] = x1;
- // Check if the abscissa of the point 2 to N-1
- // are in the segment ...
- bool ok = true;
- for (i=2; i <= nbSeg; i++)
- {
- x[i] = nextAbscissa(x[i-2], x[i-1], func, rev);
- if (x[i] - 1.0 > Precision::Confusion())
- {
- x[nbSeg] = x[i];
- ok = false;
- break;
- }
- }
- if (!ok)
- {
- // The segments are to large
- // Decrease x1 ...
- x1_too_large = x1;
- x1 = (x1_too_small+x1_too_large)/2;
- if ( x1 <= ::RealSmall() )
- return false; // break infinite loop
- continue;
- }
- // Look at the abscissa of the point N
- // which is to be close to 1.0
- // break condition --> algo converged !!
- if (1.0 - x[nbSeg] < Precision::Confusion())
- break;
+double dihotomySolve( Function& f, const double val, const double _start, const double _fin, const double eps, bool& ok )
+{
+ double start = _start, fin = _fin, start_val, fin_val; bool ok1, ok2;
+ ok1 = f.value( start, start_val );
+ ok2 = f.value( fin, fin_val );
- // not ok ...
+ if( !ok1 || !ok2 )
+ {
+ ok = false;
+ return 0.0;
+ }
- x1_too_small = x1;
+ bool start_pos = start_val>=val, fin_pos = fin_val>=val;
+ ok = true;
+
+ while( fin-start>eps )
+ {
+ double mid = ( start+fin )/2.0, mid_val;
+ ok = f.value( mid, mid_val );
+ if( !ok )
+ return 0.0;
- // Modify x1 value
+// char buf[1024];
+// sprintf( buf, "start=%f\nfin=%f\nmid_val=%f\n", float( start ), float( fin ), float( mid_val ) );
+// MESSAGE( buf );
- if (x1_too_large > 1e100)
- x1 = 2*x1;
- else
- x1 = (x1_too_small+x1_too_large)/2;
+ bool mid_pos = mid_val>=val;
+ if( start_pos!=mid_pos )
+ {
+ fin_pos = mid_pos;
+ fin = mid;
}
- xxx[rev] = x;
+ else if( fin_pos!=mid_pos )
+ {
+ start_pos = mid_pos;
+ start = mid;
+ }
+ else
+ break;
}
+ return (start+fin)/2.0;
+}
+
+static bool computeParamByFunc(Adaptor3d_Curve& C3d, double first, double last,
+ double length, bool theReverse,
+ int nbSeg, Function& func,
+ list<double>& theParams)
+{
+ OSD::SetSignal( true );
+ if( nbSeg<=0 )
+ return false;
- // average
+ MESSAGE( "computeParamByFunc" );
+
+ int nbPnt = 1 + nbSeg;
vector<double> x(nbPnt, 0.);
- for (i=0; i < nbPnt; i++)
- x[i] = (xxx[0][i] + (1.0 - xxx[1][nbPnt-i])) / 2;
+
+ x[0] = 0.0;
+ double J = func.integral( 0.0, 1.0 ) / nbSeg;
+ bool ok;
+ for( int i=1; i<nbSeg; i++ )
+ {
+ FunctionIntegral f_int( &func, x[i-1] );
+ x[i] = dihotomySolve( f_int, J, x[i-1], 1.0, 1E-4, ok );
+ if( !ok )
+ return false;
+ }
+
+ x[nbSeg] = 1.0;
+ MESSAGE( "Points:\n" );
+ char buf[1024];
+ for( int i=0; i<=nbSeg; i++ )
+ {
+ sprintf( buf, "%f\n", float(x[i] ) );
+ MESSAGE( buf );
+ }
+
+
// apply parameters in range [0,1] to the space of the curve
double prevU = first;
prevU = last;
sign = -1.;
}
- for (i = 1; i < nbSeg; i++)
+ for( int i = 1; i < nbSeg; i++ )
{
double curvLength = length * (x[i] - x[i-1]) * sign;
GCPnts_AbscissaPoint Discret( C3d, curvLength, prevU );
break;
case StdMeshers_NumberOfSegments::DT_TabFunc:
{
- TabFunction func(_vvalue[ TAB_FUNC_IND ], (bool)_ivalue[ EXP_MODE_IND ]);
+ FunctionTable func(_vvalue[ TAB_FUNC_IND ], (bool)_ivalue[ EXP_MODE_IND ]);
return computeParamByFunc(C3d, f, l, length, theReverse,
_ivalue[ NB_SEGMENTS_IND ], func,
theParams);
break;
case StdMeshers_NumberOfSegments::DT_ExprFunc:
{
- ExprFunction func(_svalue[ EXPR_FUNC_IND ].c_str(), (bool)_ivalue[ EXP_MODE_IND ]);
+ FunctionExpr func(_svalue[ EXPR_FUNC_IND ].c_str(), (bool)_ivalue[ EXP_MODE_IND ]);
return computeParamByFunc(C3d, f, l, length, theReverse,
_ivalue[ NB_SEGMENTS_IND ], func,
theParams);
